TSTP Solution File: GEO198+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO198+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 20:15:11 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 11 unt; 0 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 194 ( 71 ~; 79 |; 30 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 62 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f580,plain,
$false,
inference(avatar_sat_refutation,[],[f98,f154,f157,f169,f199,f565,f579]) ).
fof(f579,plain,
spl3_16,
inference(avatar_contradiction_clause,[],[f571]) ).
fof(f571,plain,
( $false
| spl3_16 ),
inference(resolution,[],[f564,f41]) ).
fof(f41,plain,
apart_point_and_line(intersection_point(sK0,sK2),sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f17,f35]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ( apart_point_and_line(intersection_point(sK0,sK2),sK1)
& ~ apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X1,X2] :
( apart_point_and_line(intersection_point(X0,X2),X1)
& ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( ( ~ apart_point_and_line(intersection_point(X0,X1),X2)
& convergent_lines(X0,X2)
& convergent_lines(X2,X1)
& convergent_lines(X0,X1) )
=> ~ apart_point_and_line(intersection_point(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f564,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK1)
| spl3_16 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f562,plain,
( spl3_16
<=> apart_point_and_line(intersection_point(sK0,sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f565,plain,
( ~ spl3_1
| ~ spl3_16
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f560,f197,f562,f81]) ).
fof(f81,plain,
( spl3_1
<=> convergent_lines(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f197,plain,
( spl3_8
<=> ! [X0] :
( apart_point_and_line(X0,sK2)
| ~ apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f560,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK1)
| ~ convergent_lines(sK0,sK2)
| ~ spl3_8 ),
inference(duplicate_literal_removal,[],[f555]) ).
fof(f555,plain,
( ~ apart_point_and_line(intersection_point(sK0,sK2),sK1)
| ~ convergent_lines(sK0,sK2)
| ~ convergent_lines(sK0,sK2)
| ~ spl3_8 ),
inference(resolution,[],[f212,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X0)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f48,f44]) ).
fof(f44,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
fof(f48,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X0)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| ~ convergent_lines(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_points(X2,intersection_point(X0,X1))
| ( ~ apart_point_and_line(X2,X1)
& ~ apart_point_and_line(X2,X0) )
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( convergent_lines(X0,X1)
=> ( ( apart_point_and_line(X2,X1)
| apart_point_and_line(X2,X0) )
=> distinct_points(X2,intersection_point(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).
fof(f212,plain,
( ! [X0] :
( apart_point_and_line(intersection_point(X0,sK2),sK0)
| ~ apart_point_and_line(intersection_point(X0,sK2),sK1)
| ~ convergent_lines(X0,sK2) )
| ~ spl3_8 ),
inference(resolution,[],[f198,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ apart_point_and_line(intersection_point(X0,X1),X1)
| ~ convergent_lines(X0,X1) ),
inference(resolution,[],[f49,f44]) ).
fof(f49,plain,
! [X2,X0,X1] :
( distinct_points(X2,intersection_point(X0,X1))
| ~ apart_point_and_line(X2,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f198,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| ~ apart_point_and_line(X0,sK1)
| apart_point_and_line(X0,sK0) )
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f199,plain,
( ~ spl3_4
| spl3_8
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f174,f152,f197,f144]) ).
fof(f144,plain,
( spl3_4
<=> convergent_lines(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f152,plain,
( spl3_6
<=> ! [X0] :
( apart_point_and_line(X0,sK2)
| ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f174,plain,
( ! [X0] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0)
| ~ apart_point_and_line(X0,sK1)
| ~ convergent_lines(sK0,sK1) )
| ~ spl3_6 ),
inference(resolution,[],[f153,f49]) ).
fof(f153,plain,
( ! [X0] :
( ~ distinct_points(X0,intersection_point(sK0,sK1))
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f169,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f167,plain,
( $false
| spl3_5 ),
inference(resolution,[],[f162,f39]) ).
fof(f39,plain,
convergent_lines(sK0,sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f162,plain,
( ~ convergent_lines(sK0,sK2)
| spl3_5 ),
inference(resolution,[],[f150,f45]) ).
fof(f45,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( distinct_lines(X0,X1)
| ~ convergent_lines(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( convergent_lines(X0,X1)
=> distinct_lines(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
fof(f150,plain,
( ~ distinct_lines(sK0,sK2)
| spl3_5 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl3_5
<=> distinct_lines(sK0,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f157,plain,
spl3_4,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f155,plain,
( $false
| spl3_4 ),
inference(resolution,[],[f146,f37]) ).
fof(f37,plain,
convergent_lines(sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
fof(f146,plain,
( ~ convergent_lines(sK0,sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f154,plain,
( ~ spl3_4
| ~ spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f114,f152,f148,f144]) ).
fof(f114,plain,
! [X0] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X0,sK0)
| ~ distinct_lines(sK0,sK2)
| ~ distinct_points(X0,intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1) ),
inference(resolution,[],[f89,f65]) ).
fof(f89,plain,
! [X0,X1] :
( apart_point_and_line(intersection_point(sK0,sK1),X0)
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X1,X0)
| ~ distinct_lines(X0,sK2)
| ~ distinct_points(X1,intersection_point(sK0,sK1)) ),
inference(resolution,[],[f55,f40]) ).
fof(f40,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2)
| ~ distinct_lines(X2,X3)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( distinct_lines(X2,X3)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X0,X2) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X3,X4] :
( ( distinct_lines(X3,X4)
& distinct_points(X0,X1) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X0,X4)
| apart_point_and_line(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f98,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f96,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f83,f39]) ).
fof(f83,plain,
( ~ convergent_lines(sK0,sK2)
| spl3_1 ),
inference(avatar_component_clause,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO198+2 : TPTP v8.2.0. Released v3.3.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 14:32:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (29410)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (29411)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 % (29412)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (29413)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.37 % (29415)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37 % (29416)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [1,1]
% 0.13/0.37 TRYING [2,2]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [3,3]
% 0.13/0.37 TRYING [4]
% 0.13/0.37 TRYING [3,4]
% 0.13/0.37 TRYING [3,5]
% 0.13/0.37 TRYING [5]
% 0.13/0.38 TRYING [3,6]
% 0.13/0.38 % (29417)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.38 % (29414)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.38 TRYING [6]
% 0.13/0.38 % (29413)First to succeed.
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.38 % (29413)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29410"
% 0.13/0.38 TRYING [3,7]
% 0.13/0.38 TRYING [1,1]
% 0.13/0.38 TRYING [2,2]
% 0.13/0.38 % (29413)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (29413)------------------------------
% 0.13/0.38 % (29413)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (29413)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (29413)Memory used [KB]: 1004
% 0.13/0.38 % (29413)Time elapsed: 0.016 s
% 0.13/0.38 % (29413)Instructions burned: 26 (million)
% 0.13/0.38 % (29410)Success in time 0.021 s
%------------------------------------------------------------------------------